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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.

2 votes
1 answer
345 views

comparison of eigenvalue of solution of Riccati equation

I'm trying to understand the lecture notes comparison theorems in Riemannian geometry of Eschenburg and have a problem about the proof of Rauch I. Let $E$ be an euclidean vector space and $S(E)$ the s …
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1 vote
1 answer
271 views

sectional curvature with distance between two points

I am wondering if the following statement is true or not: Let $ M $ be a complete Riemannian manifold with sectional curvature $ K $. Let $ \tilde{M} $ be the simply connected complete Riemannian man …
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